Which fundamental axioms of mathematics can be illustrated pictorially,

>>9074396

I have an autistic fantasy where I am abducted by aliens, but they're nice and don't anally probe me or anything like that. They just want to gauge my intelligence.

Among some other bric-a-brac, a collection of exactly fifty metal cubes are available for me to play with. Upon one early sit-down examination, I arrange the cubes into this pattern. They seem to be impressed, mildly amused even.

>>9074502
A human to an intelligent being capable of space travel is like a chimp to us.

>>9074396
show them deez nuts n they will immediately understand how big they r

>>9074502
That is really autistic, honestly.

>>9074396
If they are indeed AXIOMS, they cannot be proved.

Category theory is probably the closest you can get to pictorially DEFINING your AXIOMS.

A better question woulds be what proofs are there for algebra that only exist geometrically?

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>>9074502
Top kek.

>>9074396
The Pythagorean theorem is not an axiom, that's why there is proofs of it.

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>>9074569
The Steiner inellipse always intrigued me.

Take a cubic polynomial whose roots are not co-linear (they form a triangle in C).

There is a unique ellipse that can be inscribed in the triangle that touches the midpoints of the sides of the triangle.

The foci of this ellipse are located at the roots of the derivative of the cubic.

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>>9074396
OP Are you retarded? Pythagorean Theorem has a proof, it's not an axiom

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>>9074776
Lol I read that book.
I used to call my dog Bulger (STL Rams had a horrible QB by the same name)

Also try reading Steiner.

>>9074771
wew why are elliptical functions so weird?

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>>9074502
Everything went better than expected.

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>>9074842
Anything is weird to the unacquainted.

(pic: every 2 points defines a line, every 2 lines defines a point)

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>>9074396
Look how to partition a number using a Ferrers/Young diagram. If you flip across the diagonal, you get another valid diagram.

Instantly you get the theorem: The number of partitions of n having largest part k is equal to the number of partitions of n into exactly k parts.

>>9074396
Thales' Theorem. I'd post the gif but I'm away from my computer. Pretty much every old school theorem has a plain, geometric proof.

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>>9074396

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>>9074781
Really? Nobody?

>>9074396
>http://world.mathigon.org/Axioms_and_Proof
This website provides illustrations of the ZF axioms

>>9074502
wait, thats autistic? I thought everyone had those

>>9074781
>>9075437
they were right about geometers, I gotta get outa here.

>>9077034
Wow, I hope OP actually reads this. Thanks.